"The FAA and the Department of Transportation have been just ghastly in informing my committee about what possibilities there might be. I mean, just stunningly ghastly," Rockefeller said.

Speaking after a caucus lunch, the West Virginia Democrat noted a misunderstanding about the potential duration of the air traffic slowdown, which the FAA says delayed more than 1,200 flights on one day alone.

"Everybody seems to think — even in that caucus — it just goes on until ... October. This goes on forever, for years, and people are just going to go absolutely crazy in this country," Rockefeller said.

He said that he was working with Senate Majority Leader Harry Reid, D-Nev., to find some kind of legislative fix. Reid signaled he wants to try to use the all-too-familiar budget savings from the end of wars overseas to pay for turning off the sequester, at least as it relates to the FAA.

"We should do what was in one of the Ryan budgets — that is use the overseas contingency fund to delay the implementation of sequestration," Reid said.

"Sen. Rockefeller and I sent a letter to them yesterday with 18 questions asking them to respond to us about other ways in which this could be resolved as opposed to having to legislate it and take the chance that this could take a while to get through Congress," ranking member John Thune, R-S.D., said.

Thune and other Republicans say the flexibility exists to not have the air traffic tower shutdowns and other cuts causing aviation-related delays. In addition, senators in both parties have proposed stalling the tower closures. Rockefeller, however says that budgetary flexibility within FAA itself is very limited.

"There's virtually no flexibility in the FAA," Rockefeller said. "Everything is sort of about safety or its operations, it's a very untypical agency."